Question

f(x) = [x] Defined on f : R $\to$ R is a one- one function. Where [] is greatest integer function.

• A. True
• B. False

Answer 1

The correct option is B

False

If x is an integer then from [x, x+1) all the x values will give us the output of the bracket function as x. For example - from the interval [3,4) whatever we put inside the bracket function([x]) we’ll have ‘3’ as output . Since the function is giving the same output for many input values, the function is not one-one.

Alternate method – With the help of graph also we can see that while drawing lines parallel to x – axis ,they cut the graph at many points